Estimating Earth's Atmospheric Electrical Energy Potential: A Calculation Guide

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SUMMARY

The discussion focuses on estimating the electrical energy stored in Earth's atmosphere, specifically using the electric field strength of 190 V/m and an atmospheric height of 800 m. The correct approach involves treating the atmosphere as a flat slab rather than a solid sphere, which is crucial for accurate calculations. The relevant formula for energy stored, U, is derived from U = 1/2 ε₀ E², where ε₀ is the permittivity of free space (8.85e-12 F/m). Participants emphasize the importance of calculating the surface area of the Earth and the volume of the slab to arrive at the correct energy estimate.

PREREQUISITES
  • Understanding of electric field concepts, specifically V/m.
  • Familiarity with the formula for energy stored in an electric field, U = 1/2 ε₀ E².
  • Knowledge of Earth's surface area calculation.
  • Basic principles of volume calculation for geometric shapes, particularly slabs.
NEXT STEPS
  • Research the calculation of Earth's surface area and its implications for energy estimations.
  • Study the concept of electric field strength and its applications in atmospheric physics.
  • Learn about the permittivity of free space and its role in electrical energy calculations.
  • Explore advanced topics in electrostatics, including energy density in electric fields.
USEFUL FOR

This discussion is beneficial for physics students, electrical engineers, and anyone interested in atmospheric science and energy resource estimation.

fball558
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Earths potential?

Homework Statement



the problem reads as folloed
Energy prospectors from a distant planet are inspecting the Earth to decide if its electrical energy resources are worth stealing. Measurements reveal that Earth's electric field extends upward for 800 m and has an average magnitude of 190 V/m. Estimate the electrical energy stored in the atmosphere.

our TA gave us a hint and said
You may treat the atmosphere as a flat slab with an area equal to the surface area of the earth.



The Attempt at a Solution



i tried to derive an equation. i keep getting the wrong answer so please check my math and see if I am doing it wrong or just some calculation error.

i started with
U=1/2 Eo * E^2 Eo is 8.85e^-12
then i went to
U=EV substitued V=4/3pir^3 so got
U=E4/3pi*r^3
this is where i got stuck. i asked my TA and he said i was doing good so far.
i played around with some stuff and got my U (potential) as follows
U=E4pi*r^2*d
but i get the wrong answer. any help would be great ;)
thanks
 
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fball558 said:
our TA gave us a hint and said
You may treat the atmosphere as a flat slab with an area equal to the surface area of the earth.

You're using the wrong volume, it's not a solid sphere.

What is the surface area of the Earth?
What is the volume of a slab that has that area, and the thickness given in the problem statement?
 

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